A finite element method to simulate dislocation stress: A general numerical solution for inclusion problems

We developed a simple and efficient way to simulate stress from arbitrary shape dislocations within the finite element method (FEM) framework. The new method is implemented as a single-step FEM simulation using analytic solutions in an infinite medium as input terms of FEM solver with special internal boundary treatment. It is fundamentally equivalent to the multistep “image method” proposed by Van der Giessen and Needleman [Modell. Simul. Mater. Sci. Eng. 3, 689 (1995)], but the force equilibration is achieved by a single step FEM method. The singularity at the dislocation core line is removed without mesh modification, which removes many technical difficulties to couple the dislocation stress model to other process/device simulation models.